As far as I can tell, no backward compatibility. It didn't work for an application developed in Apex 4.1 and attempt to install it on Apex 4.0. Don't even think of installing it on 3.2 - no way to make it work (at least, without putting much effort into it, with a questionable result).

You'd rather upgrade all lower versions and make sure that all of them are the same (I'd suggest the latest available on OTN).